Research On Fuzzy Identification Method Of Nonlinear Dynamic System

T-S fuzzy model can describe complex nonlinear system simply and efficiently,which is widely used in the field of complex nonlinear system identification because of its universal approximation.The main work of T-S fuzzy system identification includes the selection and determination of input variables,the determination of the number of fuzzy rules,the division of fuzzy space,and the estimation of premise and conclusion parameters.The latest research results in the field of T-S fuzzy system identification mainly focus on optimizing the parameters used for training or calibrating the model.However,the selection of important input variables to reflect the optimal performance of the model has not attracted enough attention.In fact,the selection of input variables is one of the key steps of fuzzy system structure identification,which can effectively eliminate redundant information and reduce the complexity of the model.The fuzzy identification method of nonlinear dynamic system based on T-S fuzzy model is studied in this paper,focusing on the selection of important input variables and the optimization of premise parameters,so as to achieve the accuracy of model identification,reduce the complexity of the model,reduce the running time of the system and improve the online identification ability of the model.The main research contents are as follows:Based on the analysis of the structure identification and parameter identification methods of traditional T-S fuzzy model,a new method(FCM-G)is proposed to determine the premise parameters of fuzzy model by combining fuzzy c-means(FCM)algorithm with Gauss function.Firstly,Gauss function is selected as the premise membership function.Then,the cluster center automatically searched by FCM algorithm is regarded as the center of Gauss membership function.This method makes up for the defect that Gauss membership function can not automatically determine the center.Through the simulation results,compared with FCM algorithm or Gauss function for fuzzy partition,the model based on FCM-G algorithm can obtain higher identification accuracy.Aiming at the T-S fuzzy modeling problem of complex nonlinear dynamic system,a fuzzy model identification method considering the selection of important input variables is proposed.Firstly,the simplified two-stage fuzzy curves and surfaces(TSFC)method is used to select the important input variables of the model,and then the FCM clustering algorithm and triangle fuzzy partition method are used to determine the premise parameters of the fuzzy model.Compared with the existing research results,the simulation results show that the selection of important input variables has a positive impact on the identification accuracy and generalization performance of fuzzy model.In order to solve the contradiction between the model accuracy and the size of fuzzy rule base,a T-S fuzzy identification method based on TSFC-FCM-G is proposed by combining the selection of important input variables with the optimization of premise parameters.Firstly,the important input variables of the model are determined based on TSFC method;secondly,the premise parameters of the model are determined by FCM-G method;finally,the conclusion parameters are identified by recursive least square(RLS)method.The simulation results of two international standard examples and an actual variable load pneumatic loading system show that the method has the advantage of high identification accuracy without complicated iterative optimization process.For further improving the identification accuracy,a method of T-S fuzzy identification based on TSFC and modified PSO(Particle Swarm Optimization,PSO)is proposed.First,input variables are selected based on TSFC.Then,the center of Gauss function is determined by FCM algorithm,and the width of Gauss function is optimized by PSO algorithm.The effectiveness and practicability of the proposed identification method have been verified by simulation experiments.For overcoming the limitation of traditional type 1 fuzzy set in dealing with uncertainty,interval type 2 T-S fuzzy model is established based on TSFC-FCM-G for a practical hydraulic position control system.First,the important input variables of the model are determined by TSFC.Then,the premise parameters are determined by FCM-G,the reduced output is obtained by Center-of-Sets(COS)reducer.And the conclusion parameters are identified by RLS method.The simulation results show that the model has good approximation performance.